An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be \(\dots \;\)%

An alternating current is given by \(\mathrm{I}=\mathrm{I}_{\mathrm{A}} \sin \omega \mathrm{t}+\mathrm{I}_{\mathrm{B}} \cos \omega \mathrm{t}\). The r.m.s current will be ______.

A plane is in level flight at constant speed and each of its two wings has an area of \(40 \mathrm{~m}^2\). If the speed of the air is \(180 \mathrm{~km} / \mathrm{h}\) over the lower wing surface and \(252 \mathrm{~km} / \mathrm{h}\) over the upper wing surface, the mass of the plane is _______ \(\mathrm{kg}\). (Take air density to be \(1 \mathrm{~kg} \mathrm{~m}^{-3}\) and \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

The force is given in terms of time \(t\) and displacement \(x\) by the equation \({F}={A} \cos {Bx}+{C} \sin {Dt}\) The dimensional formula of \(\frac{{AD}}{{B}}\) is -

Correct Bernoulli's equation is _______. (symbols have their usual meaning)

Consider the efficiency of Carnot's engine is given by \(\eta=\frac{\alpha \beta}{\sin \theta} \log _{e} \frac{\beta x}{k T}\), where \(\alpha\) and \(\beta\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(\theta\) is angular displacement and \(x\) has the dimensions of length. Then, choose the incorrect option.

A moving coil galvanometer has a coil with \(175\, turns\) and area \(1\, cm^2\) It uses a torsion band of torsion constant \(10^{-6}\, N\, -m/rad\). The coil is placed in a magnetic field \(B\) parallel to its plane. The coil deflects by \(10\) for a current of \(1\, mA\). The value of \(B\) (in Tesla) is approximately

A student determined Young's Modulus of elasticity using the formula \(Y=\frac{M g L^{3}}{4 b d^{3} \delta} .\) The value of \(g\) is taken to be \(9.8 \,{m} / {s}^{2}\), without any significant error, his observation are as following.

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass \(({M})\)	\(1\; {g}\)	\(2\; {kg}\)
Length of bar \((L)\)	\(1\; {mm}\)	\(1 \;{m}\)
Breadth of bar \((b)\)	\(0.1\; {mm}\)	\(4\; {cm}\)
Thickness of bar \((d)\)	\(0.01\; {mm}\)	\(0.4 \;{cm}\)
Depression \((\delta)\)	\(0.01\; {mm}\)	\(5 \;{mm}\)

Then the fractional error in the measurement of \({Y}\) is

A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is \(100 g\). The time period of the motion of the particle will be (approximately) (take \(g =10\,ms ^{-2}\), radius of earth \(=6400\,km\) )

If the time period \(t\) of the oscillation of a drop of liquid of density \(d\), radius \(r\), vibrating under surface tension \(s\) is given by the formula \(t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} \) . It is observed that the time period is directly proportional to \(\sqrt {\frac{d}{s}} \) . The value of \(b\) should therefore be

The pitch and the number of divisions, on the circular scale, for a given screw gauge are \(0.5\,mm\) and \(100\) respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies \(3\) divisions below the mean line. The readings of the main scale and the circular scale for a thin sheet, are \(5.5\,mm\) and \(48\) respectively, the thickness of this sheet is